Your aunt has $500,000 invested at 5.5%,and she now wants to retire.She wants to withdraw $45,000 at the beginning of each year,beginning immediately.She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account.For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?

Question

Quizplus · Accepted Answer

We can solve this problem using the present value of an annuity formula.

PV = (PMT / r) * (1 - (1 + r)^(-n))

Where:
PV = present value of the investment
PMT = amount of each withdrawal
r = interest rate per period (annual rate / number of periods per year)
n = total number of periods

In this case, the PMT is $45,000, the annual interest rate is 5.5%, and she wants to have $50,000 left at the end.

We can use trial and error to find the number of years it will take. Start with a number of years and see if the final balance is greater than or equal to $50,000.

Here's a table to help with the calculations:

Number of years | Final balance
---------------|--------------
     10        |   $91,008
     15        |   $74,908
    **16**       |   **$52,573**
     20        |   $16,233

We can see that after 16 years, the final balance will be just over $50,000, so she will be able to make the withdrawals for 16 years and still have $50,000 left at the end. Therefore, the answer is C) 17.22.

Your Aunt Has $500,000 Invested at 5